This invention relates to methods for reducing polarization mode dispersion (PMD) in single mode optical fiber. More particularly, it relates to reducing PMD over a broad band of fiber birefringence.
It is well known that the so-called "single mode fiber" that is commonly used in communication systems is not purely single mode. Rather, two modes, with perpendicular polarizations, exist in single mode fiber. See, for example, Dandliker, R., Anisotropic and Nonlinear Optical Waveguides, C. G. Someda and G. Stegeman (editors), Elsevier, N.Y., 39-76, 1992. Mathematically, these two polarizations form an orthogonal basis set. Accordingly, any configuration of light that propagates through a single mode fiber can be represented by a linear superposition of these two modes.
If the fiber is perfectly circularly symmetric in both geometry and internal and applied stress, the two polarization modes are degenerate. They propagate with the same group velocity and have no time delay difference after traveling the same distance in the fiber. However, a practical fiber is not perfectly circularly symmetric. Imperfections such as geometric and form deformation and stress asymmetry break the degeneracy of the two modes. See, for example, Rashleigh, S. C., Journal of Lightwave Technology, LT-1:312-331, 1983. As a result, the two polarization modes propagate with different propagation constants (.beta..sub.1 and .beta..sub.2). The difference between the propagation constants is termed birefringence (.DELTA..beta.), the magnitude of the birefringence being given by the difference in the propagation constants of the two orthogonal modes: EQU .DELTA..beta.=.beta..sub.1 -.beta..sub.2 ( 1)
Birefringence causes the polarization state of light propagating in the fiber to evolve periodically along the length of the fiber. The distance required for the polarization to return to its original state is the fiber beat length (L.sub.b), which is inversely proportional to the fiber birefringence. In particular, the beat length L.sub.b is given by: EQU L.sub.b =2.pi./.DELTA..beta. (2)
Accordingly, fibers with more birefringence have shorter beat lengths and vice versa. Typical beat lengths observed in practice range from as short as 2-3 millimeters (a high birefringence fiber) to as long as 10-50 meters (a low birefringence fiber).
In addition to causing periodic changes in the polarization state of light traveling in a fiber, the presence of birefringence means that the two polarization modes travel at different group velocities, the difference increasing as the birefringence increases. The differential time delay between the two polarization modes is called polarization mode dispersion, or PMD. PMD causes signal distortion which is very harmful for high bit rate systems and analog communication systems.
Various attempts to reduce PMD have been made. One prior art method of reducing PMD involves spinning the preform during the fiber drawing process. See, for example, Barlow, et al., Applied Optics, 20:2962-2968, 1981; Payne, et al., IEEE Journal of Quantum Electronics, QE-18:477-487, 1982; Rashleigh, "Fabrication of Circularly Birefringent Single Mode Fibers," Navy Technical Disclosure Bulletin 5:7-12, 1980; and PCT Patent Publication No. WO 83/00232. The spinning causes the internal geometric and/or stress asymmetries of the fiber to rotate about the fiber's axis as one progresses down that axis. By performing the spinning during drawing, i.e., when the root of the preform is substantially molten, essentially pure rotation is performed on the fiber asymmetries, as opposed to a combination of rotation of the asymmetries and the introduction of rotational stress as would occur if the fiber were twisted after having been drawn. For a discussion of the use of twist to reduce PMD see, for example, Schuh et al., Electronics Letters, 31:1172-1173, 1995; and Ulrich, et al., Applied Optics, 18:2241-2251, 1979.
The reduction in PMD produced by spinning is proportional to the spin rate. Unfortunately, very high spin rates are generally required to deal with the asymmetries of typical fibers, e.g., spin rates greater than 5000 rpm. Spinning a preform at such rates is not a practical solution for commercial fiber production. Similarly, spinning the fiber, as opposed to the preform, at such high rates is also not particularly practical.
U.S. Pat. No. 5,298,047 (also U.S. Pat. No. 5,418,881) to Arthur C. Hart, Jr. et al. discusses reducing PMD by a relatively low rate spinning of a fiber, as opposed to a preform, during the drawing process. However, the Hart patent does not recognize that, under certain conditions, occurrences of maximal PMD reduction may be achieved. Because the Hart patent does not recognize or take advantage of these occurrences of maximal PMD reduction, the PMD reduction achieved by the method disclosed in the Hart patent is not as great as the PMD reduction achieved by the methods of the present invention.
More particularly, the Hart patent discloses a spin rate which varies in substantially a sinusoidal manner. That is, Hart's spin rate .alpha. as function of distance z along the length of Hart's fiber can be written: EQU .alpha.(z).apprxeq..alpha..sub.0 sin(2.pi.fz), (3)
where .alpha..sub.0 is Hart's spin amplitude in turns/meter and f is Hart's longitudinal frequency in inverse meters, i.e., f represents the rate at which Hart's spin rate a varies along the length of the fiber.
The term "spin function" will be used herein to describe spin rate as function of distance z, i.e., .alpha.(z), or as a function of time t, i.e., .alpha.(t), the time spin function applied to a fiber being directly derivable from the corresponding distance spin function through the fiber draw rate, which is normally constant but, in the general case, can be variable. As discussed more fully below, the spin function employed in producing a fiber, whether expressed as a function of distance or time, and the resulting spin function present in the finished fiber, expressed as a function of distance, are not in general identical because of, for example, mechanical effects, e.g., slippage, at the interface between the fiber and the apparatus used to apply the spin function to the fiber and/or preform.
Equation (3) above illustrates this difference in that the Hart patent describes its applied spin function as an oscillation, i.e., a pure sinusoid, at either 60 cycles/minute for a draw speed of 1.5 meters/second (curve 60 of Hart's FIG. 6) or 106 cycles/minute for a draw speed of 3.0 meters/second (curve 61 of Hart's FIG. 6), while the observed spin function in the fiber shown in Hart's FIG. 6 is only approximately sinusoidal. Significantly, with regard to the present invention, Hart's deviation from a pure sinusoid is not sufficient to achieve the reduced PMD disclosed herein.
In particular, in accordance with the present invention, it has been determined that a sinusoidal spin function is optimal for reducing PMD only for certain birefringence beat lengths, with the particular beat lengths for which optimization is achieved being a function of the .alpha..sub.0 and f values of the sinusoidal spin function. For other beat lengths, a sinusoidal spin function is less than optimum and can be quite poor.
Commercial fibers exhibit a wide variety of beat lengths since the geometric and stress asymmetries of such fibers vary along the length of the fiber and between different fibers. Accordingly, the substantially sinusoidal spin function of the Hart patent at best can only provide optimum PMD reduction for some fibers and/or some sections of a particular fiber.
The present invention overcomes this deficit in the Hart patent. It does so by providing improved spin functions which are not substantially sinusoidal. By means of these spin functions, greater results in terms of PMD reduction are achieved than in prior art methods. As just one example, through the use of the methods of the invention, PMD values of less than 0.1 ps/km.sup.1/2 can be achieved for a population of commercial fibers, e.g., a population comprising 100 fibers, where the members of the population, if unspun, would exhibit a range of beat lengths or alternatively, a range of PMD values, e.g., PMD values varying between fibers by as much as 1.0 ps/km.sup.1/2 and varying within a given fiber by as much as 1.0 ps/km.sup.1/2 for fibers having a length of at least 10 kilometers.